The authors have developed a consistent model for cable-beams subjected to wind flow, able to take into account, besides the axial and geometrical stiffnesses, the flexural and torsional effects. In particular, in [1] a linear model of a curved elastic pre-stressed beam, subjected to aerodynamic forces induced by wind, is formulated and, by taking into account the high slenderness of the body, it is remarkably simplified via an analysis of the magnitude orders of all terms in the equations of motion. In [2,3] the model presented in [1] is reformulated in the nonlinear range and nonlinear, reduced equations are derived along the same lines. In [4] the same nonlinear model of the cable-beam is used to investigate the nonlinear galloping behavior of a suspended cable, near the first cross-over conditions, devoting attention to the comparison between analytical and numerical approaches.

The aim of this paper is to extend the study of the bifurcation phenomena of the 2 degree-of-freedom planar model, already considered in [4], from the viewpoint of the bifurcation theory. Starting from the condition of perfect resonance, a perturbation analysis of the nonlinear problem is performed and an explicit expression of the coefficients of the discrete equations of motion, in terms of the selected parameters, is obtained. The neighborhood of the bifurcation point can be completely unfolded in sections of the space of parameters, of dimensions up to the codimension of the problem, pointing out the actual extension of the instability regions and the actual chance of existence of quasi-periodic motions.

1

A. Luongo, D. Zulli, G. Piccardo, "A linear curved-beam model for the analysis of galloping in suspended cables", Journal of Mechanics of Materials and Structures, 2(4):675-694, 2007.

2

A. Luongo, D. Zulli, G. Piccardo, "A Nonlinear Model of a Curved Beam for the Analysis of Galloping of Suspended Cables", in Proceedings of the Eighth International Conference on Computational Structures Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 93, 2006. doi:10.4203/ccp.83.93

3

A. Luongo, D. Zulli, G. Piccardo, "On the effect of twist angle on nonlinear galloping of suspended cables", Computers & Structures, 2008, in press. doi:10.1016/j.compstruc.2008.04.014

4

A. Luongo, D. Zulli, G. Piccardo. "Analytical and numerical approaches to nonlinear galloping of internally-resonant suspended cables", Journal of Sound and Vibration, 2008, in press. doi:10.1016/j.jsv.2008.03.067

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